Nearly logarithmic decay in the colloidal hard-sphere system

Nearly logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [ W. van Megen et al. Phys. Rev. E 58 6073 (1998)]. The solutions of the mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly logarithmic decay is explained as the equivalent of a β-peak phenomenon, a manifestation of the critical relaxation when the coupling between of the probe variable and the density fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula including corrections is derived from the microscopic equations of motion, which describes the experimental data for three decades in time.